It's Trivial?

Algebra Level 5

Let $$a_n$$ be defined such that it is the arithmetic mean of the p numbers before it. Let $$a_i=i, 1 \leq i \leq p$$.Let $$a_\infty=b_p$$ for such a sequence.If

$$\sum_{p=0}^{20} b_p {20 \choose p}=a*b^c$$

Then find $$a+b+c$$

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